6a^2+17a-10=0

Solution for 6a^2+17a-10=0 equation:

Simplifying
6a2 + 17a + -10 = 0

Reorder the terms:
-10 + 17a + 6a2 = 0

Solving
-10 + 17a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-10 + -3a)(1 + -2a) = 0

Subproblem 1
Set the factor '(-10 + -3a)' equal to zero and attempt to solve:

Simplifying
-10 + -3a = 0

Solving
-10 + -3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + -3a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3a = 0 + 10
-3a = 0 + 10

Combine like terms: 0 + 10 = 10
-3a = 10

Divide each side by '-3'.
a = -3.333333333

Simplifying
a = -3.333333333
Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {-3.333333333, 0.5}